Context. The ultraviolet continuum traces young stars while the near-infrared unveils older stellar populations and dust-obscured regions. Balmer emission lines provide insights into gas properties and young stellar objects but are highly affected by dust attenuation. The near-infrared Paschen lines suffer less dust attenuation and can be used to measure star formation rates (SFRs) in star-forming regions obscured by dust clouds. Aims. We present a new way of combining spectro-photometric data in order to test the robustness of the SFRs and stellar mass estimates of star-forming sources observed with JWST. We also aim to quantify the amount of differential attenuation between the interstellar medium and the birth clouds with the use of Paschen emission lines. Methods. We select 13 sources between redshifts 1 and 3 observed with HST, JWST/NIRCam and NIRSpec based on the availability of at least one Balmer and one Paschen line with S/N ≥ 5. With a newly developed version of CIGALE, we fit their hydrogen line equivalent widths (EWs) and photometric data. We assess the impacts of the removal of spectroscopic data by comparing the quality of the fits of the spectro-photometric data to those with photometric data only. We compare the single (BC03) vs binary (BPASS) stellar population models in the fitting process of spectro-photometric data. We derive the differential attenuation and explore different attenuation recipes by fitting spectro-photometric data with BC03. For each stellar model and for each input dataset (with and without EWs), we quantify the deviation on the SFRs and stellar masses from the “standard” choice. Results. The combination of spectro-photometric data provides robust constraints on the physical properties of galaxies, with a significant reduction in the uncertainties compared to using only photometric data. On average, the SFRs are overestimated and the stellar masses are underestimated when EWs are not included as input data. We find a major contribution of the H α emission line to the broadband photometric measurements of our sources, and a trend of increasing contribution with specific SFR. Using the BPASS models has a significant impact on the derived SFRs and stellar masses, with SFRs being higher by an average of 0.13 dex and stellar masses being lower by an average of 0.18 dex compared to BC03. We show that a flexible attenuation recipe provides more accurate estimates of the dust attenuation parameters, especially the differential attenuation. Finally, we reconstruct the total effective attenuation curves of the most dust-obscured galaxies in our sample.
